Variables $x$ and $y$ are related by the equation of the form $y={{x}^{a\left( x+b \right)}}$,

Question

Variables $x$ and $y$ are related by the equation of the form $y={{x}^{a\left( x+b \right)}}$, where $a$ and $b$ are constants. When $\frac{\lg y}{\lg x}$ is plotted against $x$, a straight line which passes through the point $\left( 1,-3 \right)$ and $\left( 7,3 \right)$ is obtained. Find the values of $a$ and $b$. Hence, find the value of ${{y}^{x}}$ when $x=2$.

Accepted Answer

$a = 1; \quad b = -4; \quad \text{when } x = 2, y^x = \frac{1}{16} $

Linear Law

Linear Law

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